Results 1 to 3 of 3

Math Help - Focus and directrix

  1. #1
    Member Veronica1999's Avatar
    Joined
    Jan 2010
    From
    Jupimar
    Posts
    160

    Focus and directrix

    Let the focal point F be at the origin, the horizontal line
    y = −2 be the directrix, and P = (r; θ) be equidistant from
    the focus and the directrix. Using the polar variables r and θ,
    write an equation that says that the distance from P to the
    directrix equals the distance from P to F. The configuration of
    all such P is a familiar curve; make a rough sketch of it. Then
    rearrange your equation so that it becomes r = 2/1 − sin θ,
    On which polar ray does no point appear?


    I think this should be an ellipse.
    But I am not sure what the last part of the problem is asking.
    Attached Thumbnails Attached Thumbnails Focus and directrix-direc.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Veronica1999's Avatar
    Joined
    Jan 2010
    From
    Jupimar
    Posts
    160

    Re: Focus and directrix

    I see my guess was wrong. The graph is a parabola not an ellipse.
    And the equation is undefined when theta = 90 degrees.
    Is it correct to say that no polar point appears when the ray is 90 degrees?
    Attached Thumbnails Attached Thumbnails Focus and directrix-bola.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7

    Re: Focus and directrix

    Quote Originally Posted by Veronica1999 View Post
    Is it correct to say that no polar point appears when the ray is 90 degrees?
    Yes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Parabola and Directrix and Focus.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 15th 2010, 11:19 PM
  2. Find the focus and directrix of the parabola
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: June 9th 2010, 06:56 AM
  3. Finding the focus and directrix of a parabola?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 26th 2010, 08:12 PM
  4. Focus and Directrix
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 6th 2009, 12:57 PM
  5. [SOLVED] Directrix and Focus
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: March 4th 2009, 09:53 PM

Search Tags


/mathhelpforum @mathhelpforum